This talk analyses the main candidates for a definition of climate and climate change. Five desiderata on a definition of climate are presented: it should be empirically applicable, it should correctly classify different climates, it should not depend on our knowledge, is should be applicable to the past, present and future and it should be mathematically well-defined. Then five definitions are discussed: climate as distribution over time for constant external conditions, climate as distribution over time when the external conditions vary as in reality, climate as distribution over time relative to regimes of varying external conditions, climate as the ensemble distribution for constant external conditions, and climate as the ensemble distribution when the external conditions vary as in reality. The third definition is novel and is introduced as a response to problems with existing definitions. The conclusion is that most definitions encounter serious problems and that the third definition is most promising.